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If x and y are integers greater than 1, is x a multiple of [#permalink]
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22 Jul 2007, 21:18
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If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x
2) x^2  x is a multiple of y.
Share your solutions guys, just not the answers!



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Re: DS  number properties [#permalink]
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22 Jul 2007, 21:38
asaf wrote: If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x
2) x^2  x is a multiple of y.
Share your solutions guys, just not the answers!
A for me.
stmt 1: y*(3y+7) = x
or, 3y+7 = x/y
Since, 3y+7 must be an integer, so too must be x/y. Hence, x is a multiple of y. sufficient.
stmt 2: x*(x1) = ky (k is some integer greater than 0)
This is not sufficient. e.g. x=3 and y=2; x=4 and y=2



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I think E.
I cant share my solution because I couldn't solve this easily. 1 and 2 alone look insufficient. So I made an educated guess.



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St1:
y(3y+7) = x
3y+7 = x/y
Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.
St2:
x(x1) = ym
(x/y)(x1) = m
Since m is an integer, (x1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.
Ans D



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ywilfred wrote: St1: y(3y+7) = x 3y+7 = x/y Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.
St2: x(x1) = ym (x/y)(x1) = m Since m is an integer, (x1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.
Ans D
I do not think statement 2 can be sufficient. (x1) and not x may be a multiple of y.



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sumande wrote: ywilfred wrote: St1: y(3y+7) = x 3y+7 = x/y Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.
St2: x(x1) = ym (x/y)(x1) = m Since m is an integer, (x1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.
Ans D I do not think statement 2 can be sufficient. (x1) and not x may be a multiple of y.
yeah.. missed that point. Ouch!



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Re: DS  number properties [#permalink]
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23 Jul 2007, 08:27
asaf wrote: If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x
2) x^2  x is a multiple of y.
Share your solutions guys, just not the answers!
I am going with B .
1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient.
2. x(x2) = ky . This proves x is a multiple of y .Sufficient
So B .
BTW , whats the OA ?



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Re: DS  number properties [#permalink]
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23 Jul 2007, 08:46
ashkrs wrote: asaf wrote: If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x
2) x^2  x is a multiple of y.
Share your solutions guys, just not the answers! I am going with B . 1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient. 2. x(x2) = ky . This proves x is a multiple of y .Sufficient So B . BTW , whats the OA ?
The question clearly asks if "x is a multiple of y" !!



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Re: DS  number properties [#permalink]
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24 Jul 2007, 08:19
sumande wrote: ashkrs wrote: asaf wrote: If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x
2) x^2  x is a multiple of y.
Share your solutions guys, just not the answers! I am going with B . 1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient. 2. x(x2) = ky . This proves x is a multiple of y .Sufficient So B . BTW , whats the OA ? The question clearly asks if "x is a multiple of y" !!
I think I am getting my terminology wrong. Please correct me .
If X is a multiple of Y .
I understand that as : if Y = 36 then X can be 1 2 3 4 6 12 18.



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Clear A.
x= y(3y+7) meaning x is a multiple of y.



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y*(3y+7)=x sufficient
x(x1)= y ; this would mean that y is a multiple of x. it is not the question?
my answer A.
do you have official answer??



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Joined: 21 Jun 2006
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I say A
statment in A can be factorized into
y(3y+7)=x
3y+7 must be an integer as y >1 and int
B
x(x1)=ky
where k is int
therefore, x = (k/x1)y
k/x1 need not be an integer
say if x =18, x1 = 17 and k =5 then x is not a multiple of y
Hence INSIFF



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If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x
2) x^2  x is a multiple of y.
OK lets see...
x/y=N where N is an integer?
1) Y(3Y+7)=x; x/y= (3Y+7) we are told x and y are integers...therefor RHS is an integer...which inturn means RHS is an integer...therefore X is a multiple..sufficient..
2) x(x1)=y/N ...we dont know if X or X1 is the multiple of Y..therefore insufficient...
A it is..



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Re: DS  number properties [#permalink]
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25 Jul 2007, 09:57
asaf wrote: If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x 2) x^2  x is a multiple of y
A too...........
from 1: 3y^2 + 7y = x
y (3y + 7) = x
in this case, 3y+7 is an integer. so x is a multiple of x.
from 2: x^2  x = yk
x (x 1) = yk
x (x 1) = yk
k could be or could not be x or x1. suppose, x = 4, x1=3, k =1 and y = 12. in this case x is not a multiple of y. if x = 4, x1 = 3, y = 3 and k =4, x is a multiple of y.




Re: DS  number properties
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